Regarding lights with a broken wire, if you are handy with a soldering iron, they can be fixed. First thing to do is check the light to see if it is good. Remember, LED lights are polarized. So using a "light fixer" for the original mini lights, remove the bulb from the socket and touch the leads to the light tester. If it does not light, reverse the leads and try again. If it lights good. If not discard the light.
To repair the light, First find a piece of stranded wire and strip off about 2 inches of insulation. Next, separate about 4 strands of wire and twist them together. Keep doing this until all strands have been used. Next, heat the soldering iron.
While the soldering is heating up, prepare the leads on the light. Use a small file or your wife's or girlfriend's emery board to clean the leads until shiny. Next, dip the leads in soldering flux. I use a quick clamp to hold the light steady. Tin booth leads of the light. Tinning the unbroken led will make it stronger so when you insert the bulb in the socket it should not break when you bend it. Tin the wire strands. Holding one of the tinned wire strands to the broken lead, touch the soldering iron to make the connection and when the connection has cooled cut to length.
Check the light again to make sure it still works. Too much heat from the soldering iron can kill the light. If good insert in socket and then the light set. You might have to use a small screw driver or drill bit to enlarge the hole for the repaired lead. If the light set still doesn't work, look for another bad light.
When you have a light set with bulb covers, you have to replace the light with the same color for best results or a clear or white light for ok results. Any other color will not work well.
Happy soldering and don't burn your fingers.